She didn't take her last exam. Therefore, she didn't get the Kane scholarship.

It’s because that B. mother of hers wasted all of V’s savings when she skipped out of rehab and then took the check that was the reward money from finding Duncan. Stanford gave her a lot of financial aid, but it was still more expensive than Hearst. It all came down to money. But it was also better for the story line because she wouldn’t have known anyone at Stanford. Great school, by the way. But for you younger fans, whatever school you go to, it’s really up to you what you get out of it. Stanford, Hearst, potato, potahto.

I'm pretty sure she did get the scholarship. She was wearing the valedictorian ribbon thing at graduation and she was referred to as a scholarship kid. I was confused about this too though, I think maybe she just wanted to stay closer to her dad and logan.